The development of energy-autonomous systems also requires the availability of high-performance energy storage devices. One method to store electrical energy rapidly and efficiently can be found in dielectric capacitors, provided the dielectric meets some relevant requirements. These are a high permittivity, a slim hysteresis curve, small leakage currents, and a high breakdown voltage. A class of materials that can fulfill many, if not all, of these requirements, is the so-called relaxor ferroelectrics (RF). Such RFs are created by the chemical substitution of ferroelectric materials and exhibit unique properties. These properties are not only relevant for energy storage but also for use in actuators, sensors, energy harvesting, or even novel computing devices. Despite efforts to understand RFs, the origins of their behavior are still not fully explained. This thesis aims to contribute to the discussion by using different theoretical approaches to describe RFs on an atomic level. Density functional theory (DFT) serves as the basis for all studies, allowing for the exploration of electronic structure, phonon properties, and structural deformations. As a prime example of two fundamentally different RFs, the homovalently substituted Ba(ZrxTi(1-x))O3, BZT, and the heterovalently substituted Ba(NbxTi(1-x))O3, BNT, are studied. Using DFT and comparison to experiments, substitution effects such as local volume changes, potential changes as well as the formation of defects are investigated. To study properties at finite temperatures, first-principles-based effective Hamiltonians are used for molecular dynamics (MD) simulations. First, the formalism for describing the parent system barium titanate (BaTiO3) is revised by including additional anharmonic couplings to higher-energy phonons, which yields a more accurate description of the potential energy surface. All associated parameters are parametrized using DFT calculations. Furthermore, the Hamiltonian extension's impact on various properties is studied using MD simulations, which result in a considerably better agreement with experimental data. The BaTiO3 parameterization is used as a foundation for the inclusion of substituents. An alternative scheme for describing substituents in effective Hamiltonians is introduced, which is parametrized through DFT calculations. The ensuing MD simulations reveal a high degree of agreement with experimental data and offer a thorough understanding of the occurrence of RF behavior. The effective Hamiltonians for BZT and BNT are further utilized to assess the potential of these systems in neuromorphic computing applications. The study examines the response of the systems to ultrafast THz pulses and explores the occurrence of hidden phases and polarization integration, which is a must for the realization of artificial synapses. Additionally, the thesis presents further findings on energy density in substituted BaTiO3, frequency-dependent susceptibility, and topological objects.